1) A good plot. A good example is SaiKano, which in my opinion and many others, has one of the most unattractive character designs. However, I just love it.

2) Something unique. I occasional enjoy cliche anime but what makes an anime good is non-cliche things such as Elfen Lied and Suzumiya Haruhi no Yuutsu. Man, Haibane Renmei was just...special.

3) A sense of closure. This is often overlooked but I think that it's one of the most important aspects of anime. Anime such as Naruto and Bleach are indeed good...but they didn't know when to stop. This doesn't apply to long anime, but also some that seems like they just wanted to make 24-26 episodes where it was plagued with filler-like episodes that fluctuate its quality.

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Other than that there are also some things that could make certain anime better:

4) A good mix of genres. One reason I like Avatar so much because sometimes anime's action/adventure series lack the "other genre," although some manages to put in a little comedy once in a while. Avatar, Seirei no Moribito, and Shakugan no Shana combined elements of action, adventure, comedy, romance, and drama so well that you're not just watching "the usual."

5) Animation. As much as I don't mind animation some anime just doesn't suit me because the animation is so repulsive that I just had to stop watching. Because of this, very old anime doesn't interest me, even though they're classics and such.